HOUSTON — Sen. Elizabeth Warren has turned a corner in the presidential race, emerging as not just a maven of policy plans but also someone with whom Democratic voters would like to crack open a beer.

Her rising likability among Democrats has cemented her status as a top challenger to former Vice President Joseph R. Biden, the early front-runner for the party’s presidential nomination.

A new poll confirmed the friendly factor buoying Ms. Warren’s campaign, with Democrats and Democrat-leaning voters saying they view the Massachusetts senator more favorably than any of her rivals.

She enjoyed a favorability rating of 75%, besting Mr. Biden at 71% and Sen. Bernard Sanders of Vermont at 66%, according to the NPR/PBS/Marist poll.

The spike in favorability is a startling change for Ms. Warren, who was mocked as inauthentic when she opened a beer on Instagram this year and was described in a January profile in Vanity Fair magazine as coming across on Capitol Hill as “holier than thou,” “aloof” and having a “moralizing” tone.

The warm and fuzzy feelings about Ms. Warren do not extend to Republican voters, however. Many of them revel in President Trump calling her “Pocahontas” to mock her falsely claiming Native American heritage early in her career as a lawyer and college professor.

Still, her newfound likability with Democrats helped her broaden her appeal beyond far-left ideologues to millennials, suburban women and former Hillary Clinton supporters.

It seems the more voters get to know Ms. Warren and her message the more they like her, said Vikki Brown, chairwoman of the Democratic Party in Black Hawk County, Iowa.

“I have had conversations with Elizabeth Warren, and it is like talking to your neighbor,” Ms. Brown said. “She is very accessible.”

Ms. Warren appears to have solidified herself as the “selfie” queen on the campaign trail, where she has earned a reputation for closing out her events by snapping photos with the hordes of voters who turn out to see her.

Mr. Biden’s allies appear to be taking note.

Former Pennsylvania Gov. Ed Rendell, in a Washington Post op-ed, called Ms. Warren a “hypocrite” for eschewing big-ticket fundraisers, while relying on more than $10 million from her U.S. Senate reelection campaign that came from larger donors.

In the poll, Ms. Warren also was among the least unfavorable. She tied Mayor Pete Buttigieg of South Bend, Indiana, who is known for his “nice guy” image, for the lowest unfavorable rating of 11%.

By comparison, Sen. Amy Klobuchar, who relishes her reputation for being “Minnesota nice,” scored a net favorability rating of 18%, with an 18% unfavorable score.

The bad news for Ms. Warren and the rest of the Democratic hopefuls is their likability does not bridge the country’s political divide.

Americans overall split on both Ms. Warren (40% favorable to 40% unfavorable) and Mr. Biden (44% favorable to 45% unfavorable). Mr. Sanders and Sen. Kamala D. Harris of California, who round out the top four candidates, had favorable scores that are upside down nationally, according to the pollsters.

“The best-known Democrats may be viewed well among their party faithful, but have a long way to go to connect with the national electorate,” said Lee M. Miringoff, director of the Marist College Institute for Public Opinion. “When Republicans and Republican-leaning independents are added to the mix, they each end up with high negatives.”

Even as she charms the Democratic base, the potential downside of the Warren bid was evident here in Texas.

Look no further than the Greenpeace activists who dangled on ropes beneath a bridge to block oil freighter traffic in the Houston Shipping Channel the day of the debate.

The stunt exposed the tension between the Democratic candidates, including Ms. Warren, who back a “Green New Deal” environmentalist makeover of the U.S. economy and Houston, the energy industry hub hosting their debate.

Mark P. Jones, a political science professor at nearby Rice University, said Ms. Warren and other far-left candidates could struggle to win over voters by attacking the fossil fuel industry and vowing to move the nation to 100 percent clean energy over 10 years.

“If there is one state that would be really hurt by the Green New Deal, it would be the Lone Star State,” Mr. Jones said.

Mr. Jones said down-ticket candidates, including Houston-area Rep. Lizzie Fletcher, may have to distance themselves from the party’s next presidential nominee on energy issues because so many people directly or indirectly benefit from the energy industry.

“On the one hand we have a Democratic Party that is going all-in on the Green New Deal, and yet they are holding a debate in the fossil fuel capital of the world, but the audience is a national audience and they will be focused on talking points on ending the fossil fuel industry and the only debate is whether it is five, 10 or 15 years,” he said.

The Republican Party seized on the awkward setting the Democrats chose.

“We look forward to Democrats explaining how they intend to compete in Texas while running on their socialist Green New Deal agenda of banning hamburgers and oil,” said Bob Salera, spokesman for the National Republican Congressional Committee, the campaign arm for House Republicans. “These folks are truly delusional.”

The Trump campaign also ran full-page ads in the Houston Chronicle and San Antonio Express-News highlighting how some of the Democratic contenders have called for the elimination of private insurance, higher taxes and the “abolishment of the fossil fuel industry.”

“Every single Democrat candidate has job-killing, economy-crushing policies that won’t work for America,” said Erin Perrine, Trump campaign deputy communications director. “Team Trump is here to remind them and let everyone in Houston know what a complete disaster Democrats are for America.”